One-sided commutative algebras first appeared in the paper [1]}, by Cayley, in 1857. The structure of the free bicommutative algebra of countable rank and its main numerical invariants were described by
Dzhumadildaev, Ismailov, and Tulenbaev [2]}, see also the announcement [3]}.
Bicommutative algebras were also studied in [4]}, [5]}, [6]}, and in [7]}, [8]} under the name of LR-algebras.
The algebraic and geometric classifications of 2-dimensional bicommutative algebras are given in [9]}, and that of 4-dimensional nilpotent bicommutative algebras, in [10]}.
